Loyola College B.Sc. Statistics April 2008 Resource Management Techniques Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

NO 6

 

B.Sc. DEGREE EXAMINATION – STATISTICS

THIRD SEMESTER – APRIL 2008

ST 3103 / 3100 – RESOURCE MANAGEMENT TECHNIQUES

 

 

 

Date : 07/05/2008                Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION- A

Answer all the questions.                         10×2 =  20 marks

1.Define operations research.

2.Explain the need for slack and surplus variables in an LPP.

3.Define basic solution for an LPP.

4.State the objective of  a  transportation  problem.

5.Express an assignment problem as an LPP.

6.Distinquish between CPM and PERT.

7.When is an activity in a network analysis called critical ?

8.Define degenerate solution  for a transportation problem.

9.What  is time horizon and lead time in inventory ?

10 Write a short   note on setup  and  shortage costs.

SECTION –B

Answer any five questions.                         5×8 = 40 marks

11.Obtain all the basic solutions to the following system of linear equations:

2x1 + x2 – x3 = 2

3x1 + 2x2 + x3 = 3.

12.Solve graphically the following LPP:

Max Z = 7x1 + 3x2

Subject to the constraints:

x1 + 2x2    3

x1 + x2     4

x1  5/2

x2  3/2

x10 & x2  0.

13.Find an initial solution for the following transportation problem using least cost

method:

Destination

Origin                    ————————————       Availability

D1        D2     D3      D4

——————————————————————————

O1                           1            2        1         4                        30

O                         3            3        2         1                        50

O3                           4            2        5         9                        20

Requirement         20          40      30       10

——————————————————————————-

14.Six wagons are available at six stations A,B,C,D,E and F. These are required at

stations I,II,III,IV,V and VI. The following table gives the distances(in kilometers)

between various stations:

I           II         III        IV        V         VI

A     20         23        18        10        16        20

B     50         20        17        16        15        11

C     60         30        40        55        8          7

D      6          7          10        20        100      9

E      18         19        28        17        60        70

F       9          10        20        30        40        55

How should the wagons be assigned so that the total distance covered is minimized ?

  1. A small maintenance project consists of the following 12 jobs:

Job                         Duration(in days)

  • 2

2-3                              7

2-4                               3

3-4                               3

3-5                               5

4-6                               3

5-8                               5

6-7                               8

6-10                             4

7-9                               4

8-9                               1

9-10                             1

(a) Draw the arrow diagram of the project.

(b) Determine the critical path and the project duration.

  1. Use simplex method to solve the following LPP:

Max Z = 3x1 + 2x2

Subject to the constraints:

x1+ x2   4

x1 – x2   2

x10, x20

  1. Explain the inventory control of a system.
  2. Derive a single item static model with the necessary diagram.

SECTION-C

Answer any two questions.                    2×20 = 40 marks

  1. Use big M method to

Min Z = 4x1+ 3x2

Subject to the constraints:

2x1 + x2  10

-3x1 +2x2 6

x1 + x2  6

x10,x20

  1. Consider the following transportation table showing production and transportation

costs , along with the supply and demand positions of factories/distribution centres:

M1                 M2                   M3                   M4                   Supply

——————————————————————————-

F1                          4                    6                      8                       13                   500

F2                        13                    11                    10                    8                     700

F3                        14                    4                      10                    13                   300

F4                         9                     11                    13                    3                     500

——————————————————————————–

Demand               250                 350                  1050                200

(a) Obtain an initial basic feasible solution by using VAM.

(b) Find the optimal solution for the above given problem.

  1. A project is composed of eleven activities ,the time estimates for which are given below:

——————————————————————————————————-

Activity                 optimistic time              normal time                        pessimistic time

(days)                           (days)                                    (days)

——————————————————————————————————–

1-2                                  7                                     9                                              17

1-3                                  10                                   20                                            60

1-4                                  5                                     10                                            15

2-5                                  50                                   65                                            110

2-6                                  30                                   40                                            50

3-6                                  50                                   55                                            90

3-7                                   1                                    5                                              9

4-7                                  40                                   48                                            68

5-8                                  5                                     10                                            15

6-8                                  20                                   27                                            52

7-8                                  30                                   40                                            50

(a) Draw the network diagram for the project.

(b) Find mean and variance of the activities.

(c) Determine the critical path.

(d) What is the probability of completing the project in 125 days ?

22.(a) Derive the single item static model with one price break with the necessary diagrams.

(b) LubeCar specializes in fast automobile oil change.The garage buys car oil in bulk

at $3 per gallon.A price discount of $2.50  per gallon is available if LubeCar

purchases more than 1000 gallons.The garage services approximately 150 cars per

day,and each oil change requires 1.25 gallons. LubeCar stores bulk oil at the cost

of $0.02 per gallon per day.Also the cost of placing an order for bulk oil is

$20.There is a 2 day lead time for delivery.Determine the optimal inventory policy.

 

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